Co-Registration of SAR Image Pairs for Interferometry

Current Progress & Preliminary Results An InSAR Co-registration Module “PurSAR” InSAR co-registration Coherence Evaluation Interferogram Generation DEM Processed by ASF SAR Processor + “PurSAR” + ERDAS Experiments & Analysis

Co-registration Module “PurSAR” Coarse co-registration Cross-correlation by FFT Finding coarse tie points Coarse image shift Fine co-registration Finding and filtering sub-pixel tie points 4 and 6 parameters transformation Nearest neighbor, linear, cubic, and SINC interpolators Coherence computation Interferogram generation

Coarse co-registration Defining the grids Cross-correlation computation Filtering cross-correlation peaks by peak-to-rms ratio Finding the matching points and discarding the outliers Determining the x and y shifts Shift of the slave image

Fine co-registration Defining the grids SINC up-sampling the small windows surrounding the grid points Cross-correlation computation Filtering cross-correlation peaks by peak-to-rms ratio Finding the matching points and discarding the outliers Set 4-par & 6-par transformation equations by least square Re-sampling the slave image by nearest neighbor, linear, cubic, and SINC interpolators SINC interpolators: normalized, windowed, and doppler centroid shifted

Coherence, Interferogram, and DEM Coherence evaluation Coherence image computation Coherence statistics: average, histogram, etc Coherence table: re-sampling algorithms vs. coherence magnitude Coherence comparison with ASF SAR Processor Interferogram computation DEM generation Importing co-registered SAR image pair into ERDAS Type in the orbit information Processing the SAR images into DEM in ERDAS Radar DEM evaluation

Experiments Comparison among airborne RTV SAR DEM, LIDAR and Aerial DEM ERS InSAR processing and coherence evaluation

Patch 2-AR-Roof

Armory (Building/Roof)

Armory-EW (Building/Roof)

Armory-NS (Building/Roof)

ERS InSAR processing and coherence evaluation

ERS Data description InSAR pair: a.cpx (master) and b.cpx (slave) Location: Fairbanks, Alaska Size: 5000 rows and 1000 columns; cut from a standard scene (about 25000x5000) Format: Single-look complex Processed by ASF SAR Processor The right image is only the magnitude for a.cpx

Coarse Co-registration Pair: a.cpx and b.cpx Grids: 5x3 = 15 points Peak-to-RMS Ratio = 0.004 Searching window size = 256 Use only magnitude as input for cross-correlation computation All 15 points have good peaks and no outlier Shifts: 2 in x-direction (range); 1 in y-direction (azimuth) b.cpx  b_shift.cpx

15 Pairs of Matching Points

Cross-correlation Peak for Point (700, 300)

Fine Co-registration Pair: a.cpx and b_shift.cpx Grids: 5x5 = 25 points for better performance Up-sampling ratio = 11 Up-sampling interpolator: SINC Peak-to-RMS Ratio = 0.003 Searching window size = 33 before up-sampling Cross-correlation with only magnitude Cross-correlation with complex data

Cross-correlation with Only Magnitude ---- Matching Points

Cross-correlation with Only Magnitude ---- Point (500, 100)

Cross-correlation Section with Only Magnitude ---- Point (500, 100)

Cross-correlation with Only Magnitude All 25 points have good peaks A beautiful sub-pixel peak for Point (500, 100) Azimuth direction section Solid lines Up-sampled cross-correlation 1/11th sub-pixel matching accuracy Dash lines Original pixel cross-correlation Mostly zero after coarse co-registration

Cross-correlation with Complex Data ---- Point (500, 100)

Cross-correlation with Complex Data Only 3 points passed the filter No obvious single peak Noise added by including phase data So better to use only magnitude for sub-pixel co-registration for this SAR pair; but not always

6-par Transformation

Discarding the Outliers

6-par Transformation & Discarding the Outliers 5 outliers were filtered out 6-parameter transformation equations Coefficients for y are much less significant than those for x So 4-parameter transformation is OK NofPoints = 25 X = 1.000267*x + 0.000016*y + 0.117293 StDev of X = 0.046124 Y = -0.000279*x + 1.000002*y + 0.454738 StDev of Y = 0.047559 20

4-par Transformation

Discarding the Outliers

4-par Transformation & Discarding the Outliers NofPoints = 25 X = x + 0.000229*x + 0.187576 StDev of X = 0.046135 Y = y + -0.000274*x + 0.453660 StDev of Y = 0.047165 NofPoints = 20

2D Separable SINC Function

Re-sampling Re-sampling the slave image b_shift.cpx by nearest neighbor, linear, cubic, and SINC interpolators b_shift.cpx  b_nearest_4par.cpx b_linear_4par.cpx b_cubic_4par.cpx (bicubic) b_sinc2_4par.cpx (SINC length = 2) … b_sinc20_4par.cpx (SINC length = 20)

Coherence Image ---- a.cpx vs. b.cpx

Coherence Image ---- a.cpx vs. b_shift.cpx

Coherence Image ---- a.cpx vs. b_sinc4_4par.cpx

Coherence Statistics (I) Image Pair for Coherence Computation Average Coherence a.cpx + b_corr.cpx (Co-registered and Re-sampled by ASF SAR processor) 0.695 a.cpx + b.cpx (before any co-registration) 0.191 a.cpx + b_shift.cpx (after coarse) 0.613 a.cpx + b_nearest_4par.cpx a.cpx + b_linear_4par.cpx 0.661 a.cpx + b_cubic_4par.cpx (bicubic) 0.680

Coherence Statistics (II) Image Pair for Coherence Computation Average Coherence a.cpx + b_sinc2_4par.cpx 0.691 a.cpx + b_sinc4_4par.cpx 0.701 a.cpx + b_sinc6_4par.cpx a.cpx + b_sinc8_4par.cpx 0.700 a.cpx + b_sinc10_4par.cpx 0.699 a.cpx + b_sinc14_4par.cpx a.cpx + b_sinc20_4par.cpx 0.696

Coherence Analysis ASF SAR Processor uses 4 or 6-point cubic convolution for re-sampling It is better than nearest neighbor, linear, and bicubic interpolation However, a 4-point SINC interpolator gives the better coherence than it The speed of computer has increased a lot, and the price has lowered significantly during the last 10 years; So SINC interpolation can be used practically The longer SINC is not always better for interpolation, due to the noise

Interferogram ---- a.cpx and b_sinc4_4par.cpx Single look  Multi look

Interferogram ---- Spherical Earth Correction

Interferogram ---- Phase Unwrapped

InSAR DEM in Slant Range

Final InSAR DEM